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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Cosmic Evolution in Fractional Action Cosmology

Discontinuity, Nonlinearity, and Complexity 2(2) (2013) 115--123 | DOI:10.5890/DNC.2013.04.002

Victor K. Shchigolev

Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk 432000, Russia

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For the fractional action cosmological model, derived earlier by the author from the variational principle for a fractional action functional, the exact solutions are obtained. The case of a quasi - vacuum state of matter that fills the universe is considered. Moreover, on the basis of specific ansatz proposed in this paper for the cosmological term, the class of exact solutions of the model equations is obtained. Examples for some given laws of the cosmological term evolution are provided. Besides, a formula for the effective equation of state is derived, and the deceleration parameter of the obtained models is studied.


The author would like to thank Prof. V.V. Uchaikin for his offer of the topic and valuable discussions.


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